科研之友
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摘要
We report on a systematic study of Boltzmann entropy as a function of state space size. As the state space, characterized by the number of objects N, is increased we find that identical entropies are shared by many different state space configurations. These degenerate states are called doppelganger states. A calculus is developed to predict the occurrence of these states. Theoretical and numerical analysis shows that for large N almost all configurations are doppelgangers. Boltzmann entropy is fundamental to disparate disciplines such as statistical mechanics, mixing theory, combinatorics, and information theory. Our analysis then may have some broad interest.
- 出版日期2016-11
